In countries such as the UK there are various constructional arrangements where the roof meets a side wall. In the case of the verge of a roof point, where the roof covering meets the side wall (gable triangle), running from the bottom (eaves) to the top (ridge), various methods have been used including the use of stone under-cloaking or ornate timber (barge boards) but these can be expensive.
An abutment of a roof is the point where the roof covering meets the side wall but rises above the roof. Traditionally this has been dealt with using lead sheet that is very expensive.